The phrase "moved side" could be substituted with several synonyms depending on the context. For example, the word "shifted" may be ideal in scenarios that involve slight or gentle movement. "Repositioned" could be used in cases of more significant movement or adjustment. On the other hand, "transferred" may be appropriate for instances involving the transfer of objects from one side to another. Alternatively, "switched" could be an excellent substitute for changing directions or moving from one side to another. Ultimately, the synonym used would depend on the context and the intended meaning, but there are several options to use.